/*
* INSANE - Interactive Structural Analysis Environment
*
* Copyright (C) 2003-2005
* Universidade Federal de Minas Gerais
* Escola de Engenharia
* Departamento de Engenharia de Estruturas
* 
* Author's email :    insane@dees.ufmg.br
* Author's website :  http://www.dees.ufmg.br/insane
* 
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or any later version.
* 
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
* GNU General Public License for more details.
* 
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
*/
package br.ufmg.dees.insane.model.disc.shape;

import br.ufmg.dees.insane.model.disc.element.FrameElement;
import br.ufmg.dees.insane.util.IVector;

/**
*A class representing a linear-cubic shape in one dimension and cartesian coordinates.
*
*@author Fonseca, Flavio & Pitangueira, Roque
*@version 1.0
*@since September 2003
*@see model.discrete.element.FrameElement
*/

public class LinearCubic1DCart extends Shape1DCart {
	
	private static final long serialVersionUID = 1L;

	/** Constructs a LinearCubic1DCart shape and sets its type to "LinearCubic1DCart".*/
	public LinearCubic1DCart() {
		type = "LinearCubic1DCart";
	};
	
//********************************************************************************
	
	/** Returns the shape function for this type of Shape, evaluated for the specified FrameElement and point (local X axis).
	*@return The shape function for this type of Shape, evaluated for the specified FrameElement and point (local X axis).
	*@param elm The specified FrameElement.
	*@param a The specified point (local X axis).
	*/
	public IVector getShapeFunction(FrameElement elm, double a) {
		IVector n = new IVector(6);
		double l = elm.getLength();
		double n0 = 1-(a/l);
		double n1 = a / l;
		double n2 = (2*a*a*a - 3*a*a*l + l*l*l) / (l*l*l);
		double n3 = (a*a*a*l - 2*a*a*l*l + a*l*l*l) / (l*l*l);
		double n4 = (-2*a*a*a + 3*a*a*l) / (l*l*l);
		double n5 = (a*a*a*l - a*a*l*l) / (l*l*l);
		n.setElement(0, n0);
		n.setElement(1, n1);
		n.setElement(2, n2);
		n.setElement(3, n3);
		n.setElement(4, n4);
		n.setElement(5, n5);
		return (n);
	};
	
//  ********************************************************************************
   
    /** Returns the derived shape function for this type of Shape, evaluated for the specified FrameElement and point (local X axis).
    *@return The derived shape function for this type of Shape, evaluated for the specified FrameElement and point (local X axis).
    *@param elm The specified FrameElement.
    *@param a The specified point (local X axis).
    */
    public IVector getDerivedShapeFunction(FrameElement elm, double a) {
        IVector n = new IVector(6);
        double l = elm.getLength();
        double n0 = -1/l;
        double n1 = 1/l;
        double n2 = (6*a*a - 6*a*l) / (l*l*l);
        double n3 = (3*a*a*l - 4*a*l*l + l*l*l) / (l*l*l);
        double n4 = (-6*a*a + 6*a*l) / (l*l*l);
        double n5 = (3*a*a*l - 2*a*l*l) / (l*l*l);
        n.setElement(0, n0);
        n.setElement(1, n1);
        n.setElement(2, n2);
        n.setElement(3, n3);
        n.setElement(4, n4);
        n.setElement(5, n5);
        return (n);
    };
    
//********************************************************************************
	
	/** Returns the derived shape function for this type of Shape, evaluated for the specified FrameElement and point (local X axis).
	*@return The derived shape function for this type of Shape, evaluated for the specified FrameElement and point (local X axis).
	*@param elm The specified FrameElement.
	*@param a The specified point (local X axis).
	*/
	public IVector getSecondDerivedShapeFunction(FrameElement elm, double a) {
		IVector n = new IVector(6);
		double l = elm.getLength();
		double n0 = -1/l;
		double n1 = 1/l;
        double n2 = (12*a - 6*l) / (l*l*l);
        double n3 = (6*a*l - 4*l*l ) / (l*l*l);
        double n4 = (-12*a + 6*l) / (l*l*l);
        double n5 = (6*a*l - 2*l*l) / (l*l*l);
            
		n.setElement(0, n0);
		n.setElement(1, n1);
		n.setElement(2, n2);
		n.setElement(3, n3);
		n.setElement(4, n4);
		n.setElement(5, n5);
		return (n);
	};
	
//********************************************************************************
	
	/** Returns the integrated shape function for this type of Shape, evaluated for the specified FrameElement and limits of integration.
	*@return The integrated shape function for this type of Shape, evaluated for the specified FrameElement and limits of integration.
	*@param elm The specified FrameElement.
	*@param a The initial limit of integration.
	*@param b The final limit of integration.
	*/
	public IVector getIntegratedShapeFunction(FrameElement elm, double a, double b) {
		IVector n = new IVector(6);
		double l = elm.getLength();
		double n0 = (b - b*b/(2*l)) - (a - a*a/(2*l));
		double n1 = (b*b/(2*l)) - (a*a/(2*l));
		double n2 = ((b*b*b*b/2 - b*b*b*l + b*l*l*l) - (a*a*a*a/2 - a*a*a*l + a*l*l*l)) / (l*l*l);
		double n3 = ((b*b*b*b*l/4 - 2*b*b*b*l*l/3 + b*b*l*l*l/2) - (a*a*a*a*l/4 - 2*a*a*a*l*l/3 + a*a*l*l*l/2)) / (l*l*l);
		double n4 = ((-b*b*b*b/2 + b*b*b*l) - (-a*a*a*a/2 + a*a*a*l)) / (l*l*l);
		double n5 = ((b*b*b*b*l/4 - b*b*b*l*l/3) - (a*a*a*a*l/4 - a*a*a*l*l/3)) / (l*l*l);
		n.setElement(0, n0);
		n.setElement(1, n1);
		n.setElement(2, n2);
		n.setElement(3, n3);
		n.setElement(4, n4);
		n.setElement(5, n5);
		return (n);
	};
	
//********************************************************************************
	
	/** Returns the integrated shape function multiplied by x for this type of Shape, evaluated for the specified FrameElement and limits of integration.
	*@return The integrated shape function multiplied by x for this type of Shape, evaluated for the specified FrameElement and limits of integration.
	*@param elm The specified FrameElement.
	*@param a The initial limit of integration.
	*@param b The final limit of integration.
	*/
	public IVector getIntegratedShapeFunctionMultX(FrameElement elm, double a, double b) {
		IVector n = new IVector(6);
		double l = elm.getLength();
		double n0 = (b*b/2 - b*b*b/(3*l)) - (a*a/2 - a*a*a/(3*l));
		double n1 = (b*b*b/(3*l)) - (a*a*a/(3*l));
		double n2 = ((2*b*b*b*b*b/5 - 3*b*b*b*b*l/4 + b*b*l*l*l/2) - (2*a*a*a*a*a/5 - 3*a*a*a*a*l/4 + a*a*l*l*l/2)) / (l*l*l);
		double n3 = ((b*b*b*b*b*l/5 - b*b*b*b*l*l/2 + b*b*b*l*l*l/3) - (a*a*a*a*a*l/5 - a*a*a*a*l*l/2 + a*a*a*l*l*l/3)) / (l*l*l);
		double n4 = ((-2*b*b*b*b*b/5 + 3*b*b*b*b*l/4) - (-2*a*a*a*a*a/5 + 3*a*a*a*a*l/4)) / (l*l*l);
		double n5 = ((b*b*b*b*b*l/5 - b*b*b*b*l*l/4) - (a*a*a*a*a*l/5 - a*a*a*a*l*l/4)) / (l*l*l);
		n.setElement(0, n0);
		n.setElement(1, n1);
		n.setElement(2, n2);
		n.setElement(3, n3);
		n.setElement(4, n4);
		n.setElement(5, n5);
		return (n);
	};
	
//********************************************************************************

}
